Correct Option: B

Let the width of path be x m.
Area of rectangular field = 38 × 32 = 1216 m²
Area of rectangular field without path = (38 – 2x) (32 – 2x)
= 1216 – 64x – 76x +4x²
= 1216 – 140x + 4x²
∴ Area of the path = 1216 – 1216 + 140x – 4x²
= 140x – 4x²
&there44; 140x – 4x² = 600
⇒ 4x² – 140x + 600 = 0
⇒ x² – 35x + 150 = 0
⇒ x² – 30x – 5x + 150 = 0
→ x (x– 30) –5 (x –30) = 0
→ (x– 5)(x –30) = 0
⇒ x = 5 as x ≠ 30
Aliter : Using Rule 3,
Here, L = 38 m,
B = 32 m w = ?,
Area of path = 600 m²
Area of path = 2w [L + B – 2w]
600 = 2w [38 + 32 – 2w]
300 = w (70 – 2w)
2w² – 70w + 300 = 0
w² – 35w + 150 = 0 (w – 30) (w – 5) = 0
⇒ Eitherw – 30 = 0, w = 30
But w ≠ 30
or, w – 5 = 0, w = 5
∴ w = 5 is the width of path.